Absorption spectra and frequency-dependent polarizabilities of small silicon clusters: A density functional study

The absorption spectra and frequency-dependent polarizabilities of Sin (n = 3-10) clusters have been calculated using time-dependent density functional theory (TDDFT) with 6-311+G∗ basis set and frequency-dependent coupled perturbed Hartree-Fock (CPHF) method within DFT/6-311+G∗ level, respectively. Four hybrid functionals (B3LYP, B3P86, B3PW91 and BHandHLYP) have been used to calculate the dynamic polarizabilities. With the input photon energy (Einp) ranging from 0.0 to 1.1 eV, several behaviors of the static polarizabilities hold for the dynamic values. The polarizabilities of all considered clusters exhibit the obvious anisotropic behavior and the near-resonance of Einp enhances the anisotropic behavior. The electronic origin of resonant polarizabilities of Si3 and Si4 clusters has been investigated using sum-over-states (SOS) method. The electronic transitions of π → σ and σ → n make a significant contribution to the dynamic polarizabilities of Si3 and Si4 cluster at Einp = 1.612 and 1.488 eV, respectively.